Question

This is the graph of y = sin(x). Does anyone know the second part?

Answer 1

Answer:

The resulting graph is $y = 5\cdot \sin x$.

Step-by-step explanation:

The resulting function is of the form:

$y = A\cdot \sin x + k$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$A$ - Amplitude, dimensionless.

$k$ - Midpoint value, dimensionless.

The sine function is bounded, between -1 and 1, and must be multiplied by a stretch factor. That is: $A > 0$. According to the graph, the function is bounded between 5 ($y_{max}$) and -5 ($y_{min}$), and the midpoint value ($k$) is 0. The amplitude is determined by the following calculation:

$A = \frac{y_{max}-y_{min}}{2}$

If $y_{min} = -5$ and $y_{max} = 5$, then:

$A = 5$

The resulting graph is $y = 5\cdot \sin x$.